∑ Mathematics LabLines · v4.0.4

MATHEMATICS LAB · GEOMETRY

Lines in the Cartesian Plane

Enter two equations and study lines on the Cartesian plane: intersections, angles, distances, and perpendicular projections, with every calculation explained.

Enter two linear equations in x and y. Distances use arbitrary units (u); coincident and parallel lines are detected and explained correctly.

Lines defined by equations

Enter equations for lines r and s. Supported forms include y = 2x + 1, 3x - 2y = 5 and x = 4.

Point P for distances:
P can be dragged on the graph.
Examples:

Display options

Controls and information

Drag P to change distances. Use + and − or the mouse wheel to zoom; Fit centers the construction. On touchscreens, drag P with one finger. You can also edit P's coordinates in the fields on the left.

2. Interactive line graph

Equal scale on both axes
Lines r and s
Costruzione geometrica dinamicaPiano cartesiano con le rette r e s e un punto P trascinabile.

3. Results

Updated values

4. Geometric construction of the lines

Three lines meeting at one point

5. Explained calculations

Formulas and numerical substitutions

What you can study in this version

Equations and relationships

Explicit and implicit forms, intersections, parallel, coincident, and perpendicular lines.

Angles and distances

Angle between two lines, orthogonal projections, and distance from a point to a line.

Interactive constructions

Drag P to see the perpendiculars, projection points, and results change.

This tool studies lines in the Cartesian plane, not yet conics or lines in three-dimensional space. Results are double-precision numerical approximations and do not replace formal proofs.